Hi,
Please know the difference between Basic authentication and NTLM authentication for Outlook Anywhere:
Basic authentication: If you select this authentication type, Outlook will prompt for username and password while attempting a connection with Exchange. Outlook 2010 and lator version are using "Remember my Credentials" to save credentials for Basic authentication.
NTLM authentication: If you select this authentication type, exchange does not prompt users for a user name and password. The current Windows user information on the client computer is supplied by the browser through a cryptographic exchange involving hashing with the Web server. If the authentication exchange initially fails to identify the user, the browser will prompt the user for a Windows user account user name and password. So, when Outlook is trying to connect to Exchange and if the machine is domain joined, there isnt a need to provide password.
If the saved credentials cause your Outlook problem, the issue should not be related to Exchange server. Please clear all saved credentials in Windows machine with Outlook closed, and restart Outlook without "Remember my Credentails" to have a try. Additionally, here are some articles for your reference:
https://support.microsoft.com/en-us/kb/2762344